Rate of afferent stimulus dependent synchronization and coding in coupled neurons system

Abstract

Sequences of intervals between firing times (interspike interval (ISI)) from a pair of locus ceruleus (LC) neurons coupled by axon–dendrite synapse with stimulus of constant and chaos are investigated in this paper. We analyze how the dynamical properties of chaotic input determine those of the output ISI sequences, and assess how various strength of stimulus and coupling affects the input–output relationship. The attractors constructed from delay embeddings of ISIs and of chaotic input are compared from the points of view of geometry and nonlinear dynamics characteristics, i.e., Lyapunov exponent spectrum (LES), Kaplan–York fractal dimension (KY D) and unstable periodic orbit (UPO). For the coupled LC neurons system investigated, with the moderate strength of stimulus and coupling, the synchronous oscillation of the two neurons is well preserved even if the external stimulus is chaotic; the similarity between these attractors is high only when the afferent stimulus strength is smaller and rate is lower. When these conditions are satisfied, the output two ISI sequences are reciprocally related to input signals, and their oscillation wave shape in time course can be derived from that of the input signals variation, furthermore, the similar input sequence of order of UPOs, distribution of LES and value of KY D remain in attractors reconstructed from ISI sequences. But these phenomena will disappear in higher rate of stimulus activity or in changing of the strength of stimulus and coupling, for this situation, the ISIs shows bifurcate behavior. These results may be of vital importance for any kind of information processing based on the neurons and temporal coding.